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Simulation of Sloshing-Shear Mixed Shallow Water Waves (II) Numerical Solutions

Authors: Iau-Teh Wang, Weihao Chung, Yu-Hsi Hu


This is the second part of the paper. It, aside from the core subroutine test reported previously, focuses on the simulation of turbulence governed by the full STF Navier-Stokes equations on a large scale. Law of the wall is found plausible in this study as a model of the boundary layer dynamics. Model validations proceed to include velocity profiles of a stationary turbulent Couette flow, pure sloshing flow simulations, and the identification of water-surface inclination due to fluid accelerations. Errors resulting from the irrotational and hydrostatic assumptions are explored when studying a wind-driven water circulation with no shakings. Illustrative examples show that this numerical strategy works for the simulation of sloshing-shear mixed flow in a 3-D rigid rectangular base tank.

Keywords: potential flow theory, sloshing flow, space-timefiltering, order of accuracy

Digital Object Identifier (DOI):

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[1] D. K. Lilly, "The representation of small-scale turbulence in numerical simulation experiments," Proc. IBM Sci. Comput. Symposium Environ. Sci., IBM Data Process Div., White Plains, N.Y., pp. 195-210, 1967.
[2] J. W. Deardorff, "A numerical study of three-dimensional turbulent channel flow at large Reynolds numbers," J. Fluid Mech., vol. 41, pp. 453-480, 1970.
[3] P. J. Mason, and N. S. Callen, "On the magnitude of the subgrid-scale eddy coefficient in large eddy simulations of turbulent channel flow," J. Fluid Mech., vol. 162, pp. 439-462, 1986.
[4] J. Constantin, M. G. Inclan, and M. Raschendorfer, "The energy budget of a spruce forest: field measurements and comparison with the forest-land-atmosphere model (FLAME)," J. of Hydrology, pp. 212-213, 22-35, 1998.
[5] C. Babajimopoulos, and K. Bedford, "Formulating lake models with preserve spectral statistics," J. Hydr. Div., ASCE, vol. 106, pp. 1-19, 1980.
[6] H. Schmidt, and U. Schumann, "Coherent structure of the convective boundary layer derived from large-eddy simulations," J. of Fluid Mech., vol. 200, pp. 511-565, Great Britain. 1989.
[7] C. B. Liao, M. F. Wu, and M. H. Gou, "Large eddy simulation of a round jet in a cross flow," Proceedings of the 13th hydraulic engineering conference, M14-M21, Taiwan. 2002.
[8] W. H. Chung, "Dependence of the Smagorinsky-Lilly-s constant on inertia, wind stress, and bed roughness for large eddy simulations," Journal of Mechanics, vol. 22, No. 2, pp. 125-136, 2006.
[9] G. T. Csanady, "Circulation in the Coastal Ocean," pp. 279, D. Reidel Pub. Co.., 1982.
[10] J. Amorocho, and J. J. Devries, "A new evaluation of the wind stress coefficient over water surfaces," J. Geophys. Res., vol. 85, pp. 433-442, 1980.
[11] W. H. Chung, "Dependence of the Smagorinsky-Lilly-s constant on inertia, wind stress, and bed roughness for large eddy simulations," Journal of Mechanics, vol. 22, No. 2, pp. 125-136, 2006.
[12] O. M. Faltinsen, "A numerical non-linear method of sloshing in tanks with two-dimensional flow," J. of Ship Research, vol. 18(4), pp. 224-241, 1978.
[13] T. M. Okamoto, and M. Kawahara, "Two-dimensional sloshing analysis by Lagrangian finite element method," International Journal for Numerical Methods in Fluids, vol. 11, pp. 453-477, 1990.
[14] W. Chen, M. A. Haroun, and F. Liu, "Large amplitude liquid sloshing in seismically excited tanks," Earthquake Engineering and Structural Dynamics, vol. 25, pp. 653-669, 1996.
[15] G. X. Wu, Q. W. Ma, and R. E. Taylor, "Numerical simulation of sloshing waves in a 3D tank based on a finite element method," Applied Ocean Research, vol. 20, pp. 337-355, 1998.
[16] O. M. Faltinsen, O. F. Rognebakke, and A. N. Imokha, "Resonant three-dimensional nonlinear sloshing in a square-base basin, Part 2. Effect of higher modes," J. Fluid Mech, vol. 523, pp. 199-218, 2002.
[17] O. M. Faltinsen, O. F. Rognebakke, and A. N. Timokha, "Transient and steady-state amplitudes of resonant three-dimensional sloshing in a square base thank with a finite fluid depth," Physics of Fluids, vol. 18, 012103, pp. 1-14, 2006.